Method of integration? Integration by Parts

[mathor345]

Homework Statement

Evaluate. This may not require integration by parts:

integral of x^5 sec(x^6) dx

Homework Equations

integral sec x dx = ln | sec x + tan x| + C

integral u dv = uv - integral v du

... tabular integration process

The Attempt at a Solution

u = sec x^6
du = ln | sec x^6 + tan x^6 | + C
v = 1/6x^6
dv = x^5

secx^6 * 1/6x^6 - integral 1/6x^6 * ln |sec x^6 + tan x^6 |

(secx^6)/6 * x^6 - integral (x^6 ln | sec x^6 + tan x^6 | + C)/6

... this just looks really wrong. Help! :)

 

[losiu99]

Substitute u=x^6 first. It'll be a pleasant surprise

 

[dextercioby]

As a side note, the problem sort of <warned> you about not applying the part integration method. Yet you did and ended up nowwhere. That should tell you about what to do next.

As for this part:

u = sec x^6
du = ln | sec x^6 + tan x^6 | + C

it's wrong.

 

[mathor345]

Substitute u=x^6 first. It'll be a pleasant surprise

Doh! I saw the answer as soon as I set that. Too much late night math homework after working full time really eats away at the brain, as we all see by the "backwards integration" that bigubau pointed out.

Thanks guys :)